分布式信号源参数估计技术研究
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摘要
在阵列信号处理中，由于复杂环境下的散射、反射、衍射及折射等原因造成信号源在空间发生一定的角度扩展，此时需采用参数化的分布式信号源模型进行处理。与点源模型相比，分布式信号源模型的待估计参量维数增加，计算复杂度高，并且通常要求分布源的分布函数精确已知，因此有必要研究对分布函数不敏感的低复杂度参数估计算法。针对上述问题，本文在对现有的分布源参数估计算法进行理论分析的基础上，重点研究了相干、非相干和复合式分布源参数估计技术，并提出了相应的参数估计算法，主要研究内容和成果如下：
1．研究了一维相干分布源参数估计问题。对于相干分布源的参数估计问题，通常采用的是子空间类算法。首先针对子空间类算法需要二维搜索，计算复杂度较高的问题，给出了一种基于Root-MUSIC的低复杂度相干分布源参数估计算法。然后基于分布源中心DOA和角度扩展存在的空间稀疏特性，提出了一种相干分布源中心DOA和角度扩展去耦估计算法。该算法在低信噪比、小快拍数时估计性能良好，能够分辨出来向相近的两个相干分布源，并且在估计分布源中心DOA时无需分布函数的先验信息，能用于多个分布源具有不同分布函数的情况。
2．研究了二维相干分布源参数估计问题，由于二维相干分布源需利用四维参数进行描述，通常具有较高的计算复杂度。本文基于空间频率近似模型，给出了两种低复杂度的二维相干分布源参数估计算法。首先将高阶累积量应用于二维相干分布源参数估计中，直接估计得到分布源的中心DOA和角度扩展。该算法无需谱峰搜索，计算复杂度低，并且不受阵型限制。然后将虚拟内插技术推广应用至二维相干分布源中，该算法将二维搜索转化为一维搜索，有效地降低了算法计算复杂度。并且这两种低复杂度二维相干分布源在估计分布源中心DOA时均无需相干分布源角信号密度函数精确已知，且可用于多个分布源具有不同分布函数的情况。
3．研究了一维非相干分布源参数估计问题。由于阵列无噪协方差矩阵的秩通常大于分布源个数，此时子空间类的算法不再适用。首先利用非相干分布源无噪协方差矩阵的相位信息仅受分布源中心DOA影响的特性，提出了一种非相干分布源中心DOA和角度扩展去耦估计方法。该算法在低信噪比、小快拍数时具有较好的参数估计性能，并且具有极好的分辨率。然后基于阵列无噪协方差矩阵和伪噪声子空间之间的正交性，提出了一种基于二阶锥规划的非相干分布源参数估计算法。该算法将二维搜索问题转化为一维搜索，具有较低的计算复杂度，且对分布函数误差具有稳健性。这两种非相干分布源参数估计算法在非相干分布源的角功率密度函数未知均能估计得到分布源的中心DOA，且可用于多个非相干分布源分布类型不同的情况。
4．研究了二维非相干分布源参数估计问题。与二维相干分布源类似，二维非相干分布源同样利用四维参数进行描述，在参数估计时涉及高维的非线性优化，计算量巨大。针对这个问题，提出了两种低复杂度的二维非相干分布源参数估计算法。首先将一维非相干分布源参数估计中的协方差矩阵匹配法推广应用于二维非相干分布源中，该算法无需谱峰搜索，仅需几次迭代就能估计得到分布源的二维中心DOA，具有较低的计算复杂度。然后提出了一种二维非相干分布源中心DOA和角度扩展去耦估计算法。该算法将四维搜索问题转化为两个二维搜索问题，有效地降低了计算复杂度。上述两种低复杂度的二维非相干分布源参数估计算法均不受阵型限制，并且在估计非相干分布源二维中心DOA时无需角功率密度函数的先验信息，适用于多个不同类型分布源同时存在的情况。
5．研究了复合式分布源参数估计问题。首先统一了相干分布源和非相干分布源的表示模型，然后提出了一种复合式分布源参数估计算法。该算法实现了相干分布源和非相干分布源并存时的参数估计，并在估计分布源中心DOA时无需分布源的角信号密度函数或角功率密度函数精确已知。
In the field of array signal processing, as a result of dispersion, reflection, diffraction andrefraction under complicated circumstance, impinging sources will bring about angular spreadand therefore have more complex spatial distribution characteristics than point sources. So aparameterized distributed sources model is needed. Compared with point source model,distributed source model has a higher dimension of parameters, a larger computation complexityand demands an accurate acknowledgement of distribution function of distributed sources.Consequently, it is necessary to study low complexity estimation algorithms which are notsensitive to distribution function. Take above problems into consideration, this paper makes adeep study on parameters estimation algorithms for coherent， incoherent and compositedistributed sources. The main research content is as follows:
Parameter estimation algorithms for one-dimensional coherent distributed sources arestudied. Subspace-based methods are often used to settle the estimation problem of coherentdistributed sources. So, a low complexity estimation method based on Root-MUSIC is proposedfirstly. Then, on the basis of space sparsity that exists in both central DOAs and angular spread, adecoupled estimation algorithm is given. This algorithm displays a nice performance under lowsignal-to-noise ratio (SNR) as well as under small snapshot and could distinguish closed-placeddistributed sources. Furthermore, it does not need transcendent information of distributionfunction and is suitable for distributed sources with different distribution functions.
The parameters estimation algorithms for two-dimensional coherent distributed sources areresearched. Because two-dimensional coherent distributed source is described usingfour-dimensional parameters, it has a high computation burden. Based on space frequencyapproximation model, two low complexity estimation algorithms for two-dimensional coherentdistributed sources are proposed. Firstly, cumulants is used in the estimation for two-dimensionalcoherent distributed sources. It asks for no peak search, has low complexity and has no bearingupon array structure. Then the application of interpolation array in the distributed source modelis also validated. The algorithm possesses a low-complexity through converting two-dimensionalsearch into one-dimensional search. The above two low complexity algorithms do not need theacknowledgement of accuracy angle weighting function of coherent distributed sources, so theyare suitable for multi sources with different distribution functions.
The parameters estimation algorithms for one-dimensional incoherent distributed sourcesare researched. Because the rank of noise-free covariance matrix is greater than the number ofdistributed sources, subspace based algorithms are no more applicable. Firstly, on the basis of the characteristic that the phase information of covariance matrix of distributed sources only hasrelation to the nominal DOAs of distributed sources, a kind of decoupled estimation algorithm,mis proposed. This algorithm could estimates effectively nominal DOAs and angle spread ofincoherent distributed sources. Moreover, it shows very nice estimation performance as well asresolving power under low SNR and small snapshot. Then considering the orthogonalityproperty between noise-free covariance matrix and pseudonoise subspace, a kind of SOCP basedestimation algorithm for incoherent distributed sources is presented. This algorithm convertstwo-dimensional search to one-dimensional search. it has low-complexity and robust todistribution function error. Both of the two methods mentioned above can achieve the estimationfor nominal DOAs of distributed sources without the acknowledgement of angular power densityfunction of incoherent distributed sources, and they are both suitable for multi incoherentdistributed sources with different distribution type.
The parameters estimation algorithms for two-dimensional incoherent distributed sourcesare researched. Two-dimensional incoherent distributed sources are similarly described usingfour-dimensional parameters, which results in a high computation burden due to high dimensionnonlinear optimization. In order to reduce the complexity, two low-complexity estimationalgorithms for two-dimensional incoherent distributed sources are proposed. Firstly, covariancematching estimator used in the estimation for one-dimensional incoherent distributed sources isextended to two-dimensional incoherent distributed sources. The algorithm only needs severaliterations to obtain the nominal DOAs of distributed sources without peak search, so it has a lowcomplexity. Then, a decoupled estimation algorithm for nominal DOAs of two-dimensionalincoherent distributed source is proposed based on the orthogonality property between noise-freecovariance matrix and pseudonoise subspace. In the proposed algorithm, four-dimensional searchis transformed into twice two-dimensional search, which effectively reduces the complexity. Thetwo low complexity algorithms mentioned above are both independent of array structure, andbecause it dose not need the acknowledgement of acknowledgement of angular power densityfunction of incoherent distributed sources, they are also suitable for multi distributed sources ofdifferent types.
The parameters estimation algorithm for composite distributed source is studied. Firstly,composite signal models of incoherent distributed sources and coherent distributed sources areunified, and a parameters estimation algorithm for composite distributed source is introduced.This algorithm realizes the estimation for both incoherent and coherent distributed sources at thesame time, and the acknowledgement of angular signal density function and angular powerdensity function is not necessary while during the estimation for nominal DOAs of distributedsources.
1．研究了一维相干分布源参数估计问题。对于相干分布源的参数估计问题，通常采用的是子空间类算法。首先针对子空间类算法需要二维搜索，计算复杂度较高的问题，给出了一种基于Root-MUSIC的低复杂度相干分布源参数估计算法。然后基于分布源中心DOA和角度扩展存在的空间稀疏特性，提出了一种相干分布源中心DOA和角度扩展去耦估计算法。该算法在低信噪比、小快拍数时估计性能良好，能够分辨出来向相近的两个相干分布源，并且在估计分布源中心DOA时无需分布函数的先验信息，能用于多个分布源具有不同分布函数的情况。
2．研究了二维相干分布源参数估计问题，由于二维相干分布源需利用四维参数进行描述，通常具有较高的计算复杂度。本文基于空间频率近似模型，给出了两种低复杂度的二维相干分布源参数估计算法。首先将高阶累积量应用于二维相干分布源参数估计中，直接估计得到分布源的中心DOA和角度扩展。该算法无需谱峰搜索，计算复杂度低，并且不受阵型限制。然后将虚拟内插技术推广应用至二维相干分布源中，该算法将二维搜索转化为一维搜索，有效地降低了算法计算复杂度。并且这两种低复杂度二维相干分布源在估计分布源中心DOA时均无需相干分布源角信号密度函数精确已知，且可用于多个分布源具有不同分布函数的情况。
3．研究了一维非相干分布源参数估计问题。由于阵列无噪协方差矩阵的秩通常大于分布源个数，此时子空间类的算法不再适用。首先利用非相干分布源无噪协方差矩阵的相位信息仅受分布源中心DOA影响的特性，提出了一种非相干分布源中心DOA和角度扩展去耦估计方法。该算法在低信噪比、小快拍数时具有较好的参数估计性能，并且具有极好的分辨率。然后基于阵列无噪协方差矩阵和伪噪声子空间之间的正交性，提出了一种基于二阶锥规划的非相干分布源参数估计算法。该算法将二维搜索问题转化为一维搜索，具有较低的计算复杂度，且对分布函数误差具有稳健性。这两种非相干分布源参数估计算法在非相干分布源的角功率密度函数未知均能估计得到分布源的中心DOA，且可用于多个非相干分布源分布类型不同的情况。
4．研究了二维非相干分布源参数估计问题。与二维相干分布源类似，二维非相干分布源同样利用四维参数进行描述，在参数估计时涉及高维的非线性优化，计算量巨大。针对这个问题，提出了两种低复杂度的二维非相干分布源参数估计算法。首先将一维非相干分布源参数估计中的协方差矩阵匹配法推广应用于二维非相干分布源中，该算法无需谱峰搜索，仅需几次迭代就能估计得到分布源的二维中心DOA，具有较低的计算复杂度。然后提出了一种二维非相干分布源中心DOA和角度扩展去耦估计算法。该算法将四维搜索问题转化为两个二维搜索问题，有效地降低了计算复杂度。上述两种低复杂度的二维非相干分布源参数估计算法均不受阵型限制，并且在估计非相干分布源二维中心DOA时无需角功率密度函数的先验信息，适用于多个不同类型分布源同时存在的情况。
5．研究了复合式分布源参数估计问题。首先统一了相干分布源和非相干分布源的表示模型，然后提出了一种复合式分布源参数估计算法。该算法实现了相干分布源和非相干分布源并存时的参数估计，并在估计分布源中心DOA时无需分布源的角信号密度函数或角功率密度函数精确已知。
In the field of array signal processing, as a result of dispersion, reflection, diffraction andrefraction under complicated circumstance, impinging sources will bring about angular spreadand therefore have more complex spatial distribution characteristics than point sources. So aparameterized distributed sources model is needed. Compared with point source model,distributed source model has a higher dimension of parameters, a larger computation complexityand demands an accurate acknowledgement of distribution function of distributed sources.Consequently, it is necessary to study low complexity estimation algorithms which are notsensitive to distribution function. Take above problems into consideration, this paper makes adeep study on parameters estimation algorithms for coherent， incoherent and compositedistributed sources. The main research content is as follows:
Parameter estimation algorithms for one-dimensional coherent distributed sources arestudied. Subspace-based methods are often used to settle the estimation problem of coherentdistributed sources. So, a low complexity estimation method based on Root-MUSIC is proposedfirstly. Then, on the basis of space sparsity that exists in both central DOAs and angular spread, adecoupled estimation algorithm is given. This algorithm displays a nice performance under lowsignal-to-noise ratio (SNR) as well as under small snapshot and could distinguish closed-placeddistributed sources. Furthermore, it does not need transcendent information of distributionfunction and is suitable for distributed sources with different distribution functions.
The parameters estimation algorithms for two-dimensional coherent distributed sources areresearched. Because two-dimensional coherent distributed source is described usingfour-dimensional parameters, it has a high computation burden. Based on space frequencyapproximation model, two low complexity estimation algorithms for two-dimensional coherentdistributed sources are proposed. Firstly, cumulants is used in the estimation for two-dimensionalcoherent distributed sources. It asks for no peak search, has low complexity and has no bearingupon array structure. Then the application of interpolation array in the distributed source modelis also validated. The algorithm possesses a low-complexity through converting two-dimensionalsearch into one-dimensional search. The above two low complexity algorithms do not need theacknowledgement of accuracy angle weighting function of coherent distributed sources, so theyare suitable for multi sources with different distribution functions.
The parameters estimation algorithms for one-dimensional incoherent distributed sourcesare researched. Because the rank of noise-free covariance matrix is greater than the number ofdistributed sources, subspace based algorithms are no more applicable. Firstly, on the basis of the characteristic that the phase information of covariance matrix of distributed sources only hasrelation to the nominal DOAs of distributed sources, a kind of decoupled estimation algorithm,mis proposed. This algorithm could estimates effectively nominal DOAs and angle spread ofincoherent distributed sources. Moreover, it shows very nice estimation performance as well asresolving power under low SNR and small snapshot. Then considering the orthogonalityproperty between noise-free covariance matrix and pseudonoise subspace, a kind of SOCP basedestimation algorithm for incoherent distributed sources is presented. This algorithm convertstwo-dimensional search to one-dimensional search. it has low-complexity and robust todistribution function error. Both of the two methods mentioned above can achieve the estimationfor nominal DOAs of distributed sources without the acknowledgement of angular power densityfunction of incoherent distributed sources, and they are both suitable for multi incoherentdistributed sources with different distribution type.
The parameters estimation algorithms for two-dimensional incoherent distributed sourcesare researched. Two-dimensional incoherent distributed sources are similarly described usingfour-dimensional parameters, which results in a high computation burden due to high dimensionnonlinear optimization. In order to reduce the complexity, two low-complexity estimationalgorithms for two-dimensional incoherent distributed sources are proposed. Firstly, covariancematching estimator used in the estimation for one-dimensional incoherent distributed sources isextended to two-dimensional incoherent distributed sources. The algorithm only needs severaliterations to obtain the nominal DOAs of distributed sources without peak search, so it has a lowcomplexity. Then, a decoupled estimation algorithm for nominal DOAs of two-dimensionalincoherent distributed source is proposed based on the orthogonality property between noise-freecovariance matrix and pseudonoise subspace. In the proposed algorithm, four-dimensional searchis transformed into twice two-dimensional search, which effectively reduces the complexity. Thetwo low complexity algorithms mentioned above are both independent of array structure, andbecause it dose not need the acknowledgement of acknowledgement of angular power densityfunction of incoherent distributed sources, they are also suitable for multi distributed sources ofdifferent types.
The parameters estimation algorithm for composite distributed source is studied. Firstly,composite signal models of incoherent distributed sources and coherent distributed sources areunified, and a parameters estimation algorithm for composite distributed source is introduced.This algorithm realizes the estimation for both incoherent and coherent distributed sources at thesame time, and the acknowledgement of angular signal density function and angular powerdensity function is not necessary while during the estimation for nominal DOAs of distributedsources.
引文
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